Problem:
There are seats in a row. What is the fewest number of seats that must be occupied so the next person to be seated must sit next to someone?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
In order for the fewest number of seats to be occupied, there must be someone in every third seat, beginning with and ending with . There are a total of occupied seats.
Consider some simpler cases and make a table:
In each case, the middle seat in every group of three seats must be occupied, so the desired number of occupied seats in a row of seats is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions